How come I do not receive yields from purchased tiles?

Just a bit more information on how cities and tiles work. A city can naturally grow its borders up to 5hexes away from the city hex, in every directions. It can only work the tiles up to 3hexes from the cities hex. The number of population next to the cities name is directly linked to how many 'citizens' you have, which are able to then work a tile (1citizen = 1tile) or, when no suitable / poor tiles are only available, the city by automatic will assign any citizens as 'specialists' in the city itself. These specialists work in specific buildings you have in the city (ie factory provides 2 specialist slots, +2production/turn per specialist). You can set specialist control to manual by selecting the appropriate box whilst on the city viewing page, which forces citizens to work the tiles around your city and nothing more (unless there are physically no tiles to work, in which case the inactive citizens remain unused, providing +1production per turn per citizen.

Hope this gives you some sort of insight into the mechanic :)

<<EDIT>> Forgot to mention. when assigning citizens to work tiles, if you keep clicking, you can 'lock' them into that tile. this means the city wont reassign this citizen no matter what, and this tile will forever be worked until you edit it yourself, or if you city loses too much pop from a nuke or such.

unfortunately not. you only get the yield from tiles which you are working. Therefore its more economical to only improve tiles which you can work, and strategic resources. Anything more will cost you unnecessary tile maintenance cost per turn.

Its still worth selecting the bias citizen management in most cases. ie at the start of the game, selecting production focus, then locking in food tiles is a common strat to maximize early production, as the city will work whatever production it can whilst not starving

You can collect resources (luxury and strategic) by improving the relevant tiles anywhere inside your borders. But if you want to also get the yield, you need to work the tile, and you can only work a tile within three of your city.

I like to pretend each tile outside my city is a little suburb with their own unique characteristic. The hill nomads, or the farmer delta workers or the people of the plains...Jeez I play this game too much